Finite Group Databasebeta

← C2×#20286848 #28260817

Subgroups — C2×#20286848 #28260817

Order 13568.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811314C211yesmaximal, characteristic, complemented
2C2×#16811293C211yesmaximal, characteristic
3#20286848C2116yesmaximal, direct product factor
4C2×#16810987C211yesmaximal, characteristic, complemented
5C2×#16810940C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810866C211yesmaximal, characteristic, complemented
9C2×#16810849C211yesmaximal, characteristic, complemented
10C2×#16810782C211yesmaximal, characteristic, complemented
11C2×#16810782C211yesmaximal, characteristic, complemented
12C2×#16810728C211yesmaximal, characteristic, complemented
13C2×#16810693C211yesmaximal, characteristic, complemented
14C2×#16810621C211yesmaximal, characteristic, complemented
15C2×#16810616C211yesmaximal, characteristic, complemented
16C2×C53×#460C211yesmaximal, characteristic, complemented
17C22×#11719947C2211yescharacteristic
18C22×#11719947C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719912C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811314—24no—
23#16811314C2218yescomplemented
24#16811293—24no—
25#16811293C2218yes—
26C2×#13133213—21no—
27C2×#13133211—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133207—21no—
30C2×#13133202—21no—
31C2×#13133193C2211yescharacteristic
32C2×#13133193C2211yescharacteristic
33C2×#13133189—21no—
34C2×#13133189—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×D4×Dic53—21no—
40C2×#13133175C2211yescharacteristic
41C2×#13133174—21no—
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810987C2218yescomplemented
44#16810945C2218yescomplemented
45#16810940C2218yescomplemented
46#16810931C2218yescomplemented
47#16810866C2218yescomplemented
48#16810849C2218yescomplemented
49#16810782C2218yescomplemented
50#16810782C2218yescomplemented
51#16810728C2218yescomplemented
52#16810693C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133148C2211yescharacteristic
56#16810621C2218yescomplemented
57#16810616C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133140C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133128C2211yescharacteristic
69C22×SD16×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C2×#127×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#460C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#102×C53C2211yescharacteristic
77C2×#11719947—22no—
78C2×#11719947—22no—
79C2×#11719947—24no—
80C2×#11719947—24no—
81C2×#11719947—42no—
82C2×#11719947—42no—
83C2×#11719947C2314yes—
84C2×#11719947C2314yes—
85C22×Dic106C2311yescharacteristic
86C22×D212D411yescharacteristic
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2311yescharacteristic
96C2×#11719925—24no—
97C2×#11719925C2314yes—
98C2×#11719912—42no—
99C2×#11719912C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102C2×C8×D53—42no—
103C2×C8×D53C2314yes—
104#13133213—28no—
105#13133211—28no—
106#13133209—22no—
107#13133209C2314yes—
108#13133207—28no—
109#13133202—28no—
110#13133193—22no—
111#13133193—22no—
112#13133193C2314yes—
113#13133193C2314yes—
114#13133189—28no—
115#13133189—28no—
116#13133188—22no—
117#13133188—22no—
118#13133188C2314yes—
119#13133188C2314yes—
120C4×Dic106—22no—
121C4×Dic106C2314yes—
122C4×D212D414yes—
123C4×D212C2314yes—
124D4×Dic53—28no—
125#13133175—22no—
126#13133175C2314yes—
127#13133174—28no—
128C2×C4⋊Dic53D411yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C4⋊C4×D53—22no—
139C4⋊C4×D53C2314yes—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149#13133151C2314yes—
150#13133149C2314yes—
151#13133148C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133140C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160#13133129C2314yes—
161#13133129C2314yes—
162#13133128C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53—21no—
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C2×SD16×C53—42no—
169C2×SD16×C53—42no—
170C2×SD16×C53C2314yes—
171C2×SD16×C53C2314yes—
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174#127×C53—22no—
175#127×C53C2314yes—
176C4×Q8×C53—22no—
177C4×Q8×C53C2314yes—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2311yescharacteristic
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183#102×C53C2314yes—
184#102×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C23×D53C2×D411yescharacteristic
188C23×D53C2×D411yescharacteristic
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—24no—
196C2×D4×C53—24no—
197C2×D4×C53—22no—
198C2×D4×C53—22no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—44no—
202C2×D4×C53—82no—
203C2×D4×C53C2412yes—
204C2×D4×C53C2412yes—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2411yescharacteristic
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—24no—
213C2×C22⋊D53—24no—
214C2×C22⋊D53—44no—
215C2×C22⋊D53—44no—
216C2×C22⋊D53—82no—
217C2×C22⋊D53—82no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—24no—
224C22×Dic53—44no—
225C22×Dic53—44no—
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228#11719947—28no—
229#11719947—28no—
230#11719947—44no—
231#11719947—44no—
232#11719947—48no—
233#11719947—48no—
234C2×D212—42no—
235C2×D212C2×D414yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—22no—
239C2×C4×D53—22no—
240C2×C4×D53—24no—
241C2×C4×D53—44no—
242C2×C4×D53C2×D412yes—
243C2×C4×D53C2×D412yes—
244C2×C4×D53C2412yes—
245C2×C4×D53C2412yes—
246C2×Dic106—21no—
247C2×Dic106—22no—
248C2×Dic106#4114yes—
249C2×Dic106C2412yes—
250SD16×C53—44no—
251SD16×C53—44no—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53C2412yes—
255C2×C8×C53C2412yes—
256C4⋊C4×C53—24no—
257C4⋊C4×C53—21no—
258C4⋊C4×C53C2412yes—
259C42×C53—24no—
260C42×C53C2×D412yes—
261C42×C53C2412yes—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264#11719925—28no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921C2×D414yes—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—21no—
273C4⋊Dic53C2×D414yes—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281#11719919—24no—
282#11719919—24no—
283C4×Dic53—24no—
284C4×Dic53—24no—
285C2×#88322—22no—
286C2×#88322—22no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289#11719912—44no—
290C8×D53—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53C22×D412yes—
307C22×D53C22×D412yes—
308Q8×C53—22no—
309Q8×C53—22no—
310Q8×C53—42no—
311D4×C53—22no—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—22no—
315D4×C53—48no—
316D4×C53—42no—
317D4×C53—42no—
318D4×C53—84no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—42no—
324C2×C4×C53—42no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C2×#4112yes—
329C2×C4×C53H(5,𝔽2)12yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—48no—
332C22⋊D53—48no—
333C22⋊D53—84no—
334C22⋊D53—84no—
335C2×Dic53—24no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—48no—
343C2×Dic53—48no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53C22×D412yes—
348C2×Dic53C22×D412yes—
349D212—44no—
350C4×D53—24no—
351C4×D53—24no—
352C4×D53—22no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—48no—
357Dic106—24no—
358Dic106—22no—
359Dic106C2×#4114yes—
360C8×C53—22no—
361C8×C53—22no—
362#88322—22no—
363#88322—22no—
364C2×#3317—531nomaximal, Sylow
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—84no—
372C22×C53—84no—
373C22×C53#54612yes—
374C22×C53#57512yes—
375C22×C53#57712yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—44no—
384C2×D53—44no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53#54612yes—
390C4×C53C22×#4111yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—24no—
393Dic53—22no—
394Dic53—22no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#552—531no—
399C2×#550—531no—
400#3317—5316no—
401C2×#490—531no—
402C2×#481—531no—
403C2×#482—531no—
404C2×#479—531no—
405C2×#468—531no—
406C2×#465—531no—
407C2×#460D5311yescharacteristic, complemented
408C2×#452—531no—
409C2×#452—531no—
410C2×#441—531no—
411C2×#435—531no—
412C2×#417—531no—
413C2×#416—531no—
414C2×C53—82no—
415C2×C53—82no—
416C2×C53#331714yescomplemented
417C2×C53C2×#54611yescharacteristic
418C2×C53C2×#57511yescharacteristic
419C2×C53C2×#57711yescharacteristic
420D53—42no—
421D53—42no—
422C22×#41—531no—
423C22×#41—531no—
424C22×Q16—531no—
425C22×SD16C2×D5311yescharacteristic
426C22×SD16C2×D5311yescharacteristic
427C22×M16—531no—
428C23×C8—531no—
429#552—538no—
430#552—1064no—
431#550—538no—
432#550—1064no—
433C2×#127—1061no—
434C2×#127C2×D5311yescharacteristic
435C2×#126—1061no—
436C2×#125—531no—
437C2×#125—1061no—
438C2×#123—1061no—
439C2×C22⋊Q8—531no—
440C2×C22⋊Q8—531no—
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8—531no—
446C2×C4×Q8C2×D5311yescharacteristic
447C2×C4×D4—531no—
448C2×C4×D4—1061no—
449C2×#117—531no—
450C2×#117—1061no—
451C22×C4⋊C4—531no—
452#490—538no—
453#482—538no—
454#481—538no—
455#479—538no—
456#468—538no—
457#465—538no—
458#460C2×D5318yescomplemented
459#452—538no—
460#452—538no—
461#441—538no—
462#435—538no—
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8C2×D5311yescharacteristic
467#417—538no—
468#416—538no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102C2×D5311yescharacteristic
478C2×#102C2×D5311yescharacteristic
479C2×C22⋊C8—531no—
480C2×C22⋊C8—531no—
481C2×#97—531no—
482C53C2×#331711yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—534no—
485C2×#41—1062no—
486C2×#41—1062no—
487C2×#41—1064no—
488C2×#41—1064no—
489C2×#41—2122no—
490C2×#41—2122no—
491C22×Q8—531no—
492C22×Q8C22×D5311yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—531no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4C22×D5311yescharacteristic
501C22×D4C22×D5311yescharacteristic
502C23×C4—531no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C2×Q16—534no—
508C2×Q16—1064no—
509C2×SD16—42no—
510C2×SD16—42no—
511C2×SD16C22×D5314yes—
512C2×SD16C22×D5314yes—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—534no—
518C22×C8—2122no—
519C22×C8C22×D5311yescharacteristic
520C22×C8C22×D5311yescharacteristic
521#127—22no—
522#127—1068no—
523#127C22×D5314yes—
524#126—1068no—
525#125—534no—
526#125—1068no—
527#125—1062no—
528#123—1068no—
529C22⋊Q8—534no—
530C22⋊Q8—534no—
531C22⋊Q8—1062no—
532C22⋊Q8—1062no—
533#121—534no—
534#121—534no—
535#121—1068no—
536#121—1068no—
537#121—1062no—
538#121—1062no—
539C4×Q8—22no—
540C4×Q8—534no—
541C4×Q8—1062no—
542C4×Q8C22×D5314yes—
543C4×D4—534no—
544C4×D4—534no—
545C4×D4—1068no—
546#117—534no—
547#117—1068no—
548#117—1062no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—534no—
555C2×C4⋊C4—1062no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4C22×D5311yescharacteristic
563C2×C22⋊C4—531no—
564C2×C22⋊C4—531no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C42—21no—
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8C22×D5314yes—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#102—534no—
583#102—534no—
584#102—534no—
585#102—534no—
586#102C22×D5314yes—
587#102C22×D5314yes—
588C22⋊C8—534no—
589C22⋊C8—534no—
590#97—534no—
591C24—21no—
592C24—21no—
593C24—531no—
594C24—531no—
595#41—1068no—
596#41—1068no—
597#41—2124no—
598#41—2124no—
599#41—2128no—
600#41—2128no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—534no—
605C2×Q8—532no—
606C2×Q8—1061no—
607C2×Q8—1062no—
608C2×Q8C23×D5312yes—
609C2×D4—24no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—82no—
619C2×D4—534no—
620C2×D4—1064no—
621C2×D4—1064no—
622C2×D4—1064no—
623C2×D4—1064no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—2122no—
627C2×D4—2124no—
628C2×D4—2124no—
629C2×D4C23×D5312yes—
630C2×D4C23×D5312yes—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—531no—
634C22×C4—531no—
635C22×C4—532no—
636C22×C4—532no—
637C22×C4—532no—
638C22×C4—532no—
639C22×C4—1064no—
640C22×C4—1064no—
641C22×C4—1064no—
642C22×C4—1061no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—2124no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656Q16—1068no—
657SD16—44no—
658SD16—44no—
659M16—2124no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—2124no—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—534no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—532no—
675C4⋊C4—1064no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1061no—
679C4⋊C4—1061no—
680C4⋊C4—1061no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4—1064no—
684C4⋊C4C23×D5312yes—
685C22⋊C4—534no—
686C22⋊C4—534no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C42—24no—
693C42—1064no—
694C42—1064no—
695C42D4×D5312yes—
696C42C23×D5312yes—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—532no—
706C23—532no—
707C23—1062no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—1062no—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—534no—
718Q8—1064no—
719Q8—1062no—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—42no—
726D4—42no—
727D4—84no—
728D4—4244no—
729D4—4244no—
730D4—2124no—
731D4—2128no—
732D4—2128no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—532no—
740C2×C4—532no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1064no—
744C2×C4—1062no—
745C2×C4—1064no—
746C2×C4—1064no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—2128no—
755C2×C4—2128no—
756C2×C4—2128no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4C2×D4×D5312yes—
761C2×C4C2×D4×D5312yes—
762C2×C4C2×D4×D5311yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—1062no—
769C8—1062no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—84no—
777C22—84no—
778C22—1062no—
779C22—1062no—
780C22—1062no—
781C22—1062no—
782C22—1062no—
783C22—1062no—
784C22—2124no—
785C22—2124no—
786C22#1681127012yes—
787C22#1681141912yes—
788C22#1681142912yes—
789C22C22×D4×D5311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—1062no—
795C4—1062no—
796C4—1064no—
797C4—2122no—
798C4—2122no—
799C4—2122no—
800C4#1681127012yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—82no—
804C2—82no—
805C2—2122no—
806C2—2122no—
807C2#2028684814yesdirect product factor
808C2C2×#1681127011yescharacteristic
809C2C2×#1681141911yescharacteristic
810C2C2×#1681142911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#460C2
socleC23×C53C22×D4
prime radicalC2×#16811293C2
hypercenterC2×#460D53
hypocenterC53C2×#3317
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16811314C2semidirect
3. #20286848C2direct (N × H)
4. C2×#16810987C2semidirect
5. C2×#16810940C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810866C2semidirect
9. C2×#16810849C2semidirect
10. C2×#16810782C2semidirect
11. C2×#16810782C2semidirect
12. C2×#16810728C2semidirect
13. C2×#16810693C2semidirect
14. C2×#16810621C2semidirect
15. C2×#16810616C2semidirect
16. C2×C53×#460C2semidirect
23. #16811314C22semidirect
43. #16810987C22semidirect
44. #16810945C22semidirect
45. #16810940C22semidirect
46. #16810931C22semidirect
47. #16810866C22semidirect
48. #16810849C22semidirect
49. #16810782C22semidirect
50. #16810782C22semidirect
51. #16810728C22semidirect
52. #16810693C22semidirect
56. #16810621C22semidirect
57. #16810616C22semidirect
73. C53×#460C22semidirect
407. C2×#460D53semidirect
416. C2×C53#3317semidirect
458. #460C2×D53semidirect
482. C53C2×#3317semidirect
807. C2#20286848direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168113142
C2×#168112932
#202868482
C2×#168109872
C2×#168109402
C2×#168109452
C2×#168109312
C2×#168108662
C2×#168108492
C2×#168107822
C2×#168107282
C2×#168106932
C2×#168106212
C2×#168106162
C2×C53×#4602
C2×#331753